Music 318, Winter 2007, Impulse Response Measurement
Room Impulse Response Measurementand Analysis
0 10 20 30 40 50 60 70 80 90 100-0.4
-0.2
0
0.2
0.4
0.6
0.8
1CCRMA Lobby Impulse Response
time - milliseconds
direct path
early reflections
late-field reverberation
power - dB
0
10
20
30
40
50
60
response spectra
frequency - Bark0 5 10 15 20 25
0
200
400
600
800
1000
1200
1400
Music 318, Winter 2007, Impulse Response Measurement 2
Reverberation and LTI Systems
0 10 20 30 40 50 60 70 80 90 100-0.4
-0.2
0
0.2
0.4
0.6
0.8
1CCRMA Lobby Impulse Response
time - milliseconds
direct path
early reflections
late-field reverberation
• Reflected source signals are sensitive to the detailsof the environment geometry and materials.
• Reverberation is roughly linear and time-invariant,and thus characterized by its impulse response.
(t) = L a(t){ }, (t) = L b(t){ }
L a(t) + b(t){ } = (t) + (t)
L ⋅ a(t){ } = ⋅ (t)
L a(t − ){ } = (t − )
superposition, linearity
time invariance
Music 318, Winter 2007, Impulse Response Measurement 3
0 0.5 1 1.5 2
0
0.5
1
test signal
time - seconds
ampl
itude
test signal response
time - seconds
freq
uenc
y -
kHz
0 0.5 1 1.5 20
2
4
6
8
10
LTI System Measurement
Impulsive test signal:
– Limited input amplitude poor noise rejection
s(t)
LTI system
r(t)
test sequence
measured response
n(t)
h(t)
measurement noise
s(t) = (t) → ˆ h (t) = r(t)
Music 318, Winter 2007, Impulse Response Measurement 4
LTI System Measurement Methods
• Smear impulse over time – allpass chirp, sine sweep
s(t)
LTI system
r(t)
test sequence
measured response
n(t)
h(t)
measurement noise sk (t) ∗ sk (−t) =
k∑ ⋅ (t)
→ ˆ h (t) =1
sk (−t) ∗ rk (t) k
∑
• Repeat measurement, average results – MLS, Golay
sk (t) = (t), k = 1,2,K → ˆ h (t) =
1rk (t)
k∑
s(t) = ⋅ a(t), a(−t) ∗ a(t) = (t) → ˆ h (t) =1
s(−t) ∗ r(t)
Music 318, Winter 2007, Impulse Response Measurement 5
Sine Sweep Measurement
0 0.5 1 1.5 2-1
0
1
test signal
time - seconds
ampl
itude
test signal response
time - seconds
freq
uenc
y -
kHz
0 0.5 1 1.5 20
2
4
6
8
10
0 0.5 1 1.5 2
0
0.5
1
processed chirp
time - seconds
ampl
itude
estimated impulse response
time - secondsfr
eque
ncy
- kH
z
0 0.5 1 1.5 20
2
4
6
8
10
• Frequency trajectory (t), t [0,T], sine sweep s(t):
s(t) = sin (t), (t) = ( )d0
t
∫
Music 318, Winter 2007, Impulse Response Measurement 6
s(t) ∗ (t) ≈ (t), bandlimited to ∈[ 0, T ]
Sine Sweep Generation
• Monotonic frequency trajectory (t), t [0,T]
• Sine sweep s(t), "inverse" (t):
s(t) = sin (t), (t) = ( )d0
t
∫
• For (t) monotonic, slowly varying, [ 0, T]
(t) = v(−t) ⋅ sin (−t), v(t) = 2d
dt
Music 318, Winter 2007, Impulse Response Measurement 7
E{ ˆ h (t)} = h(t) + (t) ∗E{n(t)} = h(t)
Measurement Bias, SNR Gain
• Impulse response estimate
ˆ h (t) = (t) ∗ r(t) = [ (t) ∗ s(t)] ∗ h(t) + (t) ∗ n(t)
= h(t) + (t) ∗ n(t)
• Expected value (zero-mean noise assumed)
• SNR gain (sweep, noise uncorrelated)
Γ( ) ∝1/ 2d
dt
s(t)
LTI system
r(t)
test sequence
measured response
n(t)
h(t)
measurement noise
Music 318, Winter 2007, Impulse Response Measurement 8
sine sweep response
time - seconds
freq
uenc
y -
kHz
0.2 0.4 0.6 0.8 1 1.2 1.4 1.60
5
10
15
20
Nonlinear Measurement Example
• Speaker generates harmonic series
r(t) = g(t) ∗ ( k)sin k ( )d0
t
∫( )k
∑ , k (t) = k ⋅ (t)
s(t)(·)
speaker
g(t)
room
r(t)
Music 318, Winter 2007, Impulse Response Measurement 9
exponential sweep response
time - seconds
freq
uenc
y -
kHz
0.2 0.4 0.6 0.8 1 1.2 1.4 1.610-1
100
101
Exponential Sweep (Farina, 2000)
• Sweep harmonic trajectories isomorphic; appear astime-offset exponential sweeps
(t) = 0 ⋅e t, =1
Tlog 0
T
= (t + 1 log k)
k (t) = k ⋅ 0 ⋅e t
= 0 ⋅e(t + 1 log k)
Music 318, Winter 2007, Impulse Response Measurement 10
0 0.5 1 1.5 2-0.5
0
0.5
1processed response
time - secondsam
plitu
de
exponential sweep response
time - seconds
freq
uenc
y -
kHz
0 0.5 1 1.5 210-1
100
101
Exponential Sweep Response
• Processing using the sweep inverse produces a series oftime-shifted responses, one for each harmonic present.
• The "linear" response is the impulse response; the remainingresponses are used to estimate THD.
Music 318, Winter 2007, Impulse Response Measurement 11
0 0.5 1 1.5 2-0.5
0
0.5
1processed response
time - seconds
ampl
itude
exponential sweep response
time - seconds
freq
uenc
y -
kHz
0 0.5 1 1.5 210-1
100
101
System Linear Portion
• Power nonlinearities generate even/odd harmonicseries, depending on the sense of p; e.g., for p odd,
cosp t = 21− p p
k
cos( p − 2k)k =0
( p −1)/2
∑ ⋅ t
→ The time-separated "linear" response may not bethe desired system linear portion.
s(t)g(t)
room
(·)
mic preamp
r(t)
preamp nonlinearity
Music 318, Winter 2007, Impulse Response Measurement 12
0 500 1000 1500-0.5
0
0.5sine sweep, s(t)
ampl
itude
freq
uenc
y -
kHz
sine sweep spectrogram
0 200 400 600 800 10000
5
10
0 500 1000 1500-0.5
0
0.5sine sweep response, r(t)
time - milliseconds
ampl
itude
time - milliseconds
freq
uenc
y -
kHz
sine sweep response spectrogram
0 200 400 600 800 10000
5
10
0 5 10 15 20 25 30 35 40-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2measured impulse response
time - milliseconds
ampl
itude
Acoustic Tube Measurment Example
s(t)
r(t)
ˆ h (t)
Music 318, Winter 2007, Impulse Response Measurement 13
0 500 1000 1500-0.5
0
0.5sine sweep, s(t)
ampl
itude
freq
uenc
y -
kHz
sine sweep spectrogram
0 200 400 600 800 10000
5
10
0 500 1000 1500 2000-1
-0.5
0
0.5
1sine sweep response, r(t)
time - milliseconds
ampl
itude
time - milliseconds
freq
uenc
y -
kHz
sine sweep response spectrogram
0 500 1000 1500 20000
5
10
0 100 200 300 400 500 600 700 800 900 1000-0.04
-0.02
0
0.02
0.04
0.06
0.08measured impulse response
time - milliseconds
ampl
itude
CCRMA Lobby Measurment Example
s(t)
r(t)
ˆ h (t)
Music 318, Winter 2007, Impulse Response Measurement 14
Impulse Response Measurement Analysis
0 10 20 30 40 50 60 70 80 90 100-0.4
-0.2
0
0.2
0.4
0.6
0.8
1CCRMA Lobby Impulse Response
time - milliseconds
direct path
early reflections
late-field reverberation
• The impulse response of a reverberant environmentwill often have a direct path, followed by a few earlyreflections and the late-field reverberation.
Music 318, Winter 2007, Impulse Response Measurement 15
0 20 40 60 80 100 120 140 160 180 200-0.5
0
0.5
1impulse response
time - milliseconds
0 20 40 60 80 100 120 140 160 180 2000
0.2
0.4
0.6
0.8
1
echo density profile, 20-msec. frames.
time - msec.
Echo Density Profile
• Echo density can be measured along an impulseresponse by comparing the percentage of tapslying outside the local standard deviation to thatexpected for Gaussian noise.
Music 318, Winter 2007, Impulse Response Measurement 16
Echo Density Psychoacoustics
0 100 200 300 400 500 600 700 800 900-2
0
2
4
6impulse responses
time - milliseconds
0 100 200 300 400 500 600 700 800 9000
0.2
0.4
0.6
0.8
1
echo density profile, 20-msec. frames.
time - msec.
Music 318, Winter 2007, Impulse Response Measurement 17
Late-Field Time-Frequency Analysis
power - dB
0
10
20
30
40
50
60
response spectra
frequency - Bark0 5 10 15 20 25
0
200
400
600
800
1000
1200
1400
Music 318, Winter 2007, Impulse Response Measurement 18
Late-Field Time-Frequency Analysis
10-1 100 101-80
-70
-60
-50
-40
-30
-20
-10
0response spectra, 70-msec. interval between frames.
frequency - kHz
Music 318, Winter 2007, Impulse Response Measurement 19
Late-Field Time-Frequency Analysis
0 200 400 600 800 1000 1200 1400-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
0response power spectrum, Bark-spaced frequencies.
time - milliseconds
Music 318, Winter 2007, Impulse Response Measurement 20
0 200 400 600 800 1000 1200 1400-120
-100
-80
-60
-40
-20
0measured, modeled response energy profile
time - milliseconds
Late-Field Decay Rate Estimation
Music 318, Winter 2007, Impulse Response Measurement 21
Equalization and Reverberation Time
10-1 100 101
-10
-5
0q - resonance spectrum.
frequency - kHz
10-1 100 10110-1
100
101T_{60} - 60-dB decay time.
frequency - kHz
Music 318, Winter 2007, Impulse Response Measurement 22
EMT140 Plate Reverberator Responses
power - dB
0
10
20
30
40
50
60
EMT140B response spectra, various damping settings
frequency - Bark0 5 10 15 20 25
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
10-1 100 10110-1
100
101T_{60} - 60-dB decay time, various low-frequency absorption settings.
frequency - kHz
impulse response spectrograms
late-field decay times